Check if the frequency of all the digits in a number is same in Python

A number is considered balanced when the frequency of all its digits is the same. For example, in the number 562256, each digit (5, 6, and 2) appears exactly 2 times, making it a balanced number.

In this article, we'll explore different methods to check if a number is balanced in Python.

Using Dictionary to Count Frequencies

We can convert the number to a string and use a dictionary to count the frequency of each digit ?

from collections import defaultdict

def is_balanced(num):
    number = str(num)
    
    # Count frequency of each digit
    freq = defaultdict(int)
    for digit in number:
        freq[digit] += 1
    
    # Get all frequency values
    freq_values = set(freq.values())
    
    # If all digits have same frequency, set will have only one element
    return len(freq_values) == 1

# Test the function
num = 562256
print(f"Number: {num}")
print(f"Is balanced: {is_balanced(num)}")

Number: 562256
Is balanced: True

Using Counter from Collections

The Counter class provides a more concise way to count digit frequencies ?

from collections import Counter

def is_balanced_counter(num):
    # Count frequencies of all digits
    digit_counts = Counter(str(num))
    
    # Get unique frequency values
    frequencies = set(digit_counts.values())
    
    # Return True if all digits have same frequency
    return len(frequencies) == 1

# Test with multiple examples
test_numbers = [562256, 112233, 123456, 1122]

for num in test_numbers:
    result = is_balanced_counter(num)
    print(f"{num}: {'Balanced' if result else 'Not Balanced'}")

562256: Balanced
112233: Balanced
123456: Balanced
1122: Balanced

Using List Comprehension

A more compact approach using list comprehension and set operations ?

def is_balanced_compact(num):
    num_str = str(num)
    # Count frequency of each unique digit
    frequencies = [num_str.count(digit) for digit in set(num_str)]
    # Check if all frequencies are the same
    return len(set(frequencies)) == 1

# Test with unbalanced number
test_cases = [562256, 12233, 111222, 12345]

for num in test_cases:
    result = is_balanced_compact(num)
    digit_counts = {digit: str(num).count(digit) for digit in set(str(num))}
    print(f"Number: {num}")
    print(f"Digit frequencies: {digit_counts}")
    print(f"Result: {'Balanced' if result else 'Not Balanced'}")
    print("-" * 30)

Number: 562256
Digit frequencies: {'5': 2, '2': 2, '6': 2}
Result: Balanced
------------------------------
Number: 12233
Digit frequencies: {'1': 1, '2': 2, '3': 2}
Result: Not Balanced
------------------------------
Number: 111222
Digit frequencies: {'1': 3, '2': 3}
Result: Balanced
------------------------------
Number: 12345
Digit frequencies: {'1': 1, '2': 1, '4': 1, '5': 1, '3': 1}
Result: Balanced
------------------------------

Comparison of Methods

Conclusion

To check if a number is balanced, count the frequency of each digit and verify all frequencies are equal. The Counter method offers the cleanest solution, while the dictionary approach provides better understanding of the algorithm.